The Moment of Inertia of the Disc is represented by
. (Correct answer: A)
Let suppose that the Disk is a Rigid Body whose mass is uniformly distributed. The Moment of Inertia of the element is equal to the Moment of Inertia of the entire Disk minus the Moment of Inertia of the Hole, that is to say:
(1)
Where:
- Moment of inertia of the Disk.
- Moment of inertia of the Hole.
Then, this formula is expanded as follows:
(1b)
Dimensionally speaking, Mass is directly proportional to the square of the Radius, then we derive the following expression for the Mass removed by the Hole (
):
![\frac{m}{M} = \frac{R^{2}}{4\cdot R^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7Bm%7D%7BM%7D%20%3D%20%5Cfrac%7BR%5E%7B2%7D%7D%7B4%5Ccdot%20R%5E%7B2%7D%7D)
![m = \frac{1}{2}\cdot M](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20M)
And the resulting equation is:
![I = \frac{1}{2}\cdot M\cdot R^{2} -\frac{1}{2}\cdot \left(\frac{1}{4}\cdot M \right) \cdot \left(\frac{1}{4}\cdot R^{2} \right)](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20M%5Ccdot%20R%5E%7B2%7D%20-%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cleft%28%5Cfrac%7B1%7D%7B4%7D%5Ccdot%20M%20%5Cright%29%20%5Ccdot%20%5Cleft%28%5Cfrac%7B1%7D%7B4%7D%5Ccdot%20R%5E%7B2%7D%20%5Cright%29)
![I = \frac{1}{2} \cdot M\cdot R^{2} - \frac{1}{32}\cdot M\cdot R^{2}](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ccdot%20M%5Ccdot%20R%5E%7B2%7D%20-%20%5Cfrac%7B1%7D%7B32%7D%5Ccdot%20M%5Ccdot%20R%5E%7B2%7D)
![I = \frac{15}{32}\cdot M\cdot R^{2}](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7B15%7D%7B32%7D%5Ccdot%20M%5Ccdot%20R%5E%7B2%7D)
The moment of inertia of the Disc is represented by
. (Correct answer: A)
Please see this question related to Moments of Inertia: brainly.com/question/15246709
Answer:
Animals are classifield as two main groups in the animal kingdom : Vertebrates and invertebrates .
Explanation:
keep it up....
The strength of the gravitational force between two objects depends on two factors, mass and distance. the force of gravity the masses exert on each other. If one of the masses is doubled, the force of gravity between the objects is doubled. increases, the force of gravity decreases.
Answer: They behave the same because, according to the principle of equivalence, the laws of physics work the same in all frames of reference.
Explanation:
According to the equivalence principle postulated by Einstein's Theory of General Relativity, acceleration in space and gravity on Earth have the same effects on objects.
To understand it better, regarding to the equivalence principle, Einstein formulated the following:
A gravitational force and an acceleration in the opposite direction are equivalent, both have indistinguishable effects. Because the laws of physics must be accomplished in all frames of reference.
Hence, according to general relativity, gravitational force and acceleration in the opposite direction (an object in free fall, for example) have the same effect. This makes sense if we deal with gravity not as a mysterious atractive force but as a geometric effect of matter on spacetime that causes its deformation.